1382400 has 144 divisors (see below), whose sum is σ = 5077800. Its totient is φ = 368640.

The previous prime is 1382393. The next prime is 1382419. The reversal of 1382400 is 42831.

It is a happy number.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as 6! ⋅ 5! ⋅ (2!)^{4}.

It is a tau number, because it is divible by the number of its divisors (144).

It is a super-2 number, since 2×1382400^{2} = 3822059520000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 276478 + ... + 276482.

2^{1382400} is an apocalyptic number.

1382400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1382400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2538900).

1382400 is an abundant number, since it is smaller than the sum of its proper divisors (3695400).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

1382400 is an equidigital number, since it uses as much as digits as its factorization.

1382400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 41 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 1382400 is about 1175.7550765359. The cubic root of 1382400 is about 111.3981320067.

The spelling of 1382400 in words is "one million, three hundred eighty-two thousand, four hundred".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54 60 64 72 75 80 90 96 100 108 120 128 135 144 150 160 180 192 200 216 225 240 256 270 288 300 320 360 384 400 432 450 480 512 540 576 600 640 675 720 768 800 864 900 960 1024 1080 1152 1200 1280 1350 1440 1536 1600 1728 1800 1920 2048 2160 2304 2400 2560 2700 2880 3072 3200 3456 3600 3840 4320 4608 4800 5120 5400 5760 6144 6400 6912 7200 7680 8640 9216 9600 10240 10800 11520 12800 13824 14400 15360 17280 18432 19200 21600 23040 25600 27648 28800 30720 34560 38400 43200 46080 51200 55296 57600 69120 76800 86400 92160 115200 138240 153600 172800 230400 276480 345600 460800 691200 1382400

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